Q.Lime trees and sap
I think my lime tree is dripping sap onto the ground below it. There are hundreds of flies on the garden furniture, trampoline, etc. I was wondering what’s caused this (only happened in the last three days – lots of heat and lots of rain), and how to fix the problem – short and long term? It’s a HUGE tree, by the way, so I don’t think simply spraying it is an option.
The highest probability is that your tree is infested with aphids, which are dripping honeydew. Read more here: https://www.gardeningknowhow.com/plant-problems/pests/insects/aphids-tree-disease.htm
Unfortunately, you're probably going to have to spray the tree to get rid of the aphids. Here's some more information on their control: https://www.gardeningknowhow.com/plant-problems/pests/homemade-aphid-control-a-natural-way-to-kill-aphids.htm